STOCKHOLM—Swedish artist Lars Vilks was comparing notes a few months ago with the editor-in-chief of the French satirical newspaper Charlie Hebdo. Both had faced death threats over drawings of the Muslim Prophet Muhammad.

Mr. Vilks said the editor, Gérard Biard, appeared reassured that the police patrols, bodyguards and other security measures around the paper’s new Paris office would keep him and his co-workers safe.